The Angels got right-hander Nick Tropeano and minor league catcher Carlos Perez in the deal Wednesday.
The 26-year-old Conger played 80 games with 70 starts last season for the Angels. A first-round pick in 2006, Conger hit .221 with four homers and a career-high 25 RBIs.
Houston general manager Jeff Luhnow says: "We scouted him extensively this year as a divisional opponent and feel he brings a unique skill set to our organization."
Tropeano went 1-3 with a 4.57 ERA in four games for Houston in 2014. He spent most of the season at Triple-A Oklahoma City, where he was 9-5 with a 3.03 ERA in 23 games.
Perez spent last season in Triple-A, hitting .259 with six homers and 34 RBIs.
The 30-year-old Ramos pitched 43 games for the Rays last season, including seven starts. He was 2-6 with a 3.70 ERA. He was tied for seventh among AL relievers with 13 outings of at least two innings.
Ramos is 5-11 with one save and a 3.90 ERA in 186 games for San Diego and Tampa Bay.
The 23-year-old Sappington went a combined 4-11 with a 6.02 ERA in Double-A and Single-A last season.
Information from The Associated Press was used in this report.